Linear adaptive equalizers having a plurality of taps are widely used in digital communication receivers in order to provide correction for multipath channel distortion. Adaptive algorithms, such as the least mean squares (LMS) algorithm, are implemented in order to determine the weight values for the taps of the equalizer. Such adaptive algorithms are easy to implement and provide reasonably good performance. However, under difficult channel conditions, these algorithms may fail to provide tap weights that converge to the desired values.
It is well known that this failure may be avoided if the tap weights, instead of being initialized to values of zero as is often done, are initialized at least somewhat close to their final desired values based on a knowledge of the channel impulse response (CIR). An estimate of the channel impulse response may be derived from an a priori known training signal periodically transmitted prior to, and/or along with, the unknown data. One such system with this feature is specified in the ATSC 8VSB standard for digital terrestrial television broadcasting.
The channel impulse response is typically estimated in a receiver by cross-correlating the training signal as received with a representation of the known transmitted training signal stored in the receiver. The Z-transform of the estimated channel impulse response is derived and inverted. From the inverted Z-transform, a vector is formed having a plurality of elements, and these elements are used to initialize a corresponding number of tap weights of the equalizer.
A conventional linear adaptive equalizer 10 that utilizes a transversal filter 12 is shown in FIG. 1. The transversal filter 12 comprises a plurality of taps Nff whose weights are applied to the received signal in order to eliminate the effects of multipath from the received signal. If it is assumed, for example, that the multipath communication channel is purely anti-causal (precursor response only), then the cursor position may be placed at the extreme right (last tap) of the transversal filter 12. The transversal filter 12 includes a plurality of outputs 141 through 14n and a corresponding plurality of multipliers 161 through 16n. The signal on each of the outputs 141 through 14n is multiplied by a corresponding tap weight from a conventional tap weight update algorithm 18 (such as an LMS) by a corresponding one of the multipliers 161 through 16n. The outputs from the multipliers 161 through 16n are added together by an adder 20, and the output from the adder 20 is supplied as an output of the conventional linear adaptive equalizer 10. The output from the adder 20 is also supplied to a decision directed/blind module 22 that compares the filter output with either the known training signal, when the known training signal is being received, or likely corrected data decisions when the unknown data instead of the known training signal are being received. This comparison forms an error signal e that is used by the conventional tap weight update algorithm 18 to update the linear tap weights so as to minimize the value of the error e.
During training, and as described above, the conventional tap weight update algorithm 18 typically estimates the channel impulse response by a-periodically cross-correlating the training signal as received with a stored version of the known training signal. If s[k] is defined as the stored known training sequence for k=0 . . . (L−1), and if u[k] is defined as received data sampled at the symbol rate, with u[o] being the first received training symbol in the received signal, the cross-correlation is given by the following equation:
                                          h            ⁡                          [              i              ]                                =                                    ∑                              k                =                0                                            L                -                1                                      ⁢                                          s                ⁡                                  [                  k                  ]                                            ⁢                              u                ⁡                                  [                                      k                    +                    i                                    ]                                                                    ,                              for            -                          N              a                                ≤          i          ≤                      N            c                                              (        1        )            where Nc is the length of the causal response of the channel (post ghosts), and Na is the length of the anti-causal channel response (pre-ghosts).
The conventional tap weight update algorithm 18 then determines the Z-transform of h[i] and inverts the Z-transform in order to determine the tap weights that are supplied to the multipliers 161 through 16n.
The present invention provides a novel technique for forming a more accurate estimate of the channel impulse response h[i]. Alternatively and/or additionally, the present invention provides a novel technique for determining the inverse of the Z-transform of the estimated channel impulse response h[i].